Simple Harmonic Motion and equilibrium of springs

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Homework Help Overview

The discussion revolves around a system in equilibrium involving springs and a pulley, specifically focusing on the period of oscillation for a mass in simple harmonic motion (SHM). Participants are exploring the relevant equations and concepts related to oscillation and restoring forces.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the setup of force diagrams and geometric relations, questioning the dimensional correctness of the equations used. There is an inquiry into the derivation of the period for a mass on a spring and the nature of the restoring force when the mass is disturbed from equilibrium.

Discussion Status

The discussion is active, with participants providing guidance on dimensional analysis and prompting for further details on attempts made. There is an ongoing exploration of concepts without a clear consensus on the next steps or solutions.

Contextual Notes

Participants are addressing the need for additional equations related to time and are considering the implications of the combined spring constant in their analysis. The original poster's attempts at force diagrams have not yielded satisfactory results, indicating potential gaps in understanding or application.

Mateus Buarque
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The figure below shows a system in equillibrium. The pulley and the springs (both with constants "k") are ideal. The period of oscillation of the mass A is given by:

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Relevant equations:

F = -kx (SHM)

I tried to do a "force diagram" and set up some geometric relations but it´s not working.
 
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Hi,

You can start with discarding the answers that have the wrong dimension.
Your relevant equation needs a few colleagues: at least one with a dimension of time.
Would you know how the period for a simple mass hanging from a spring comes about ?
What is the restoring force for a disturbance from equilibrium in your system ?

Oh, and I notice you haven't been welcomed, so here goes:
Hello Mateus, :welcome: !
 
Mateus Buarque said:
I tried to do a "force diagram" and set up some geometric relations but it´s not working.
Please show the details of what you have tried.
 
BvU said:
Hi,

You can start with discarding the answers that have the wrong dimension.
Your relevant equation needs a few colleagues: at least one with a dimension of time.
Would you know how the period for a simple mass hanging from a spring comes about ?
What is the restoring force for a disturbance from equilibrium in your system ?

Oh, and I notice you haven't been welcomed, so here goes:
Hello Mateus, :welcome: !

Thank you but no answer has a wrong dimension, cause they are all in the form of a constant*root(m/k), which is correct!
 
Oops, so that doesn't help. Now how about the 'combined' spring constant ? What is the restoring force if I pull down the mass over a small distance ##x## ?
 

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